With global CO2 concentrations increasing every year as industry continues to grow, carbon capture, utilization and geological storage (CCUS) technology is a key solution to mitigating the effects of climate change and a key pillar in achieving global carbon neutrality. CO2 injection alters the geological stress distribution, and the mechanical behavior of the fault is an important factor in assessing its stability. In this paper, the Johansen formation in the Norwegian North Sea is taken as the research object, and a geomechanical model is established to assess the stability of CO2 injection faults for long-term storage. And the three parameters of vertical displacement, shear safety coefficient, and tensile safety coefficient generated in the fault are selected as evaluation indexes to measure the mechanical closure of the fault, and to judge whether the fault generates shear damage and tensile fracture breakage.Throughout the process, the shear safety coefficient of the rock is always positive, and no shear damage occurs on this surface fault. The tensile safety coefficient inside the fault is always in non-negative value, the rock structure is not easy to be damaged, and the tensile fracture damage will not occur inside the fault.